<!doctype html public "-//w3c//dtd html 4.0 transitional//en"
          "http://www.w3.org/TR/REC-html40/loose.dtd">
<html>
<head>
  <meta http-equiv="Content-Type"
        content="text/html; charset=iso-8859-1">
  <meta name="Author"
        content="David Turner">
  <title>FreeType Glyph Conventions</title>
</head>

<body text="#000000"
      bgcolor="#FFFFFF"
      link="#0000EF"
      vlink="#51188E"
      alink="#FF0000">

<h1 align=center>
  FreeType Glyph Conventions
</h1>

<h2 align=center>
  Version&nbsp;2.1
</h2>

<h3 align=center>
  Copyright&nbsp;1998-2000 David Turner (<a
  href="mailto:david@freetype.org">david@freetype.org</a>)<br>
  Copyright&nbsp;2000, 2007 The FreeType Development Team (<a
  href="mailto:devel@freetype.org">devel@freetype.org</a>)
</h3>

<center>
<table width="65%">
<tr><td>

  <center>
  <table width="100%"
         border=0
         cellpadding=5>
  <tr bgcolor="#CCFFCC"
      valign=center>
    <td align=center
        width="30%">
      <a href="glyphs-1.html">Previous</a>
    </td>
    <td align=center
        width="30%">
      <a href="index.html">Contents</a>
    </td>
    <td align=center
        width="30%">
      <a href="glyphs-3.html">Next</a>
    </td>
  </tr>
  </table>
  </center>

  <p><hr></p>

  <table width="100%">
  <tr bgcolor="#CCCCFF"
      valign=center><td>
    <h2>
      II. Glyph Outlines
    </h2>
  </td></tr>
  </table>

  <p>This section describes the way scalable representations of glyph images,
  called outlines, are used by FreeType as well as client applications.</p>

    <a name="section-1">
    <h3>
      1. Pixels, points and device resolutions
    </h3>

    <p>Though it is a very common assumption when dealing with computer
    graphics programs, the physical dimensions of a given pixel (be it for
    screens or printers) are not squared.  Often, the output device, be it a
    screen or printer, exhibits varying resolutions in both horizontal and
    vertical direction, and this must be taken care of when rendering
    text.</p>

    <p>It is thus common to define a device's characteristics through two
    numbers expressed in <em>dpi</em> (dots per inch).  For example, a
    printer with a resolution of 300x600&nbsp;dpi has 300&nbsp;pixels per
    inch in the horizontal direction, and 600 in the vertical one.  The
    resolution of a typical computer monitor varies with its size
    (15"&nbsp;and 17"&nbsp;monitors don't have the same pixel sizes at
    640x480), and of course the graphics mode resolution.</p>

    <p>As a consequence, the size of text is usually given in
    <em>points</em>, rather than device-specific pixels.  Points are a
    simple <em>physical</em> unit, where 1&nbsp;point&nbsp;=&nbsp;1/72th of
    an inch, in digital typography.  As an example, most Roman books are
    printed with a body text whose size is somewhere between 10 and
    14&nbsp;points.</p>

    <p>It is thus possible to compute the size of text in pixels from the
    size in points with the following formula:</p>

    <center>
      <tt>pixel_size = point_size * resolution / 72</tt>
    </center>

    <p>The resolution is expressed in <em>dpi</em>.  Since horizontal and
    vertical resolutions may differ, a single point size usually defines a
    different text width and height in pixels.</p>

    <p><em>Unlike what is often thought, the "size of text in pixels" is not
    directly related to the real dimensions of characters when they are
    displayed or printed.  The relationship between these two concepts is a
    bit more complex and relate to some design choices made by the font
    designer.  This is described in more detail in the next sub-section (see
    the explanations on the EM square).</em></p>


    <a name="section-2">
    <h3>
      2. Vectorial representation
    </h3>

    <p>The source format of outlines is a collection of closed paths called
    <em>contours</em>.  Each contour delimits an outer or inner
    <em>region</em> of the glyph, and can be made of either <em>line
    segments</em> or <em>B&eacute;zier arcs</em>.</p>

    <p>The arcs are defined through <em>control points</em>, and can be
    either second-order (these are <em>conic</em> B&eacute;ziers) or
    third-order (<em>cubic</em> B&eacute;ziers) polynomials, depending on
    the font format.  Note that conic B&eacute;ziers are usually called
    <em>quadratic</em> B&eacute;ziers in the literature.  Hence, each point
    of the outline has an associated flag indicating its type (normal or
    control point).  And scaling the points will scale the whole
    outline.</p>

    <p>Each glyph's original outline points are located on a grid of
    indivisible units.  The points are usually stored in a font file as
    16-bit integer grid coordinates, with the grid origin's being at (0,0);
    they thus range from -16384 to&nbsp;16383.  (Even though point
    coordinates can be floats in other formats such as Type&nbsp;1, we will
    restrict our analysis to integer values for simplicity).</p>

    <p><em>The grid is always oriented like the traditional mathematical
    two-dimensional plane, i.e., the <i>X</i>&nbsp;axis from the left to the
    right, and the <i>Y</i>&nbsp;axis from bottom to top.</em></p>

    <p>In creating the glyph outlines, a type designer uses an imaginary
    square called the <em>EM square</em>.  Typically, the EM square can be
    thought of as a tablet on which the characters are drawn.  The square's
    size, i.e., the number of grid units on its sides, is very important for
    two reasons:</p>

    <ul>
      <li>
        <p>It is the reference used to scale the outlines to a given text
        dimension.  For example, a size of 12pt at 300x300&nbsp;dpi
        corresponds to 12*300/72&nbsp;=&nbsp;50&nbsp;pixels.  This is the
        size the EM square would appear on the output device if it was
        rendered directly.  In other words, scaling from grid units to
        pixels uses the formula:</p>

        <p><center>
          <tt>pixel_size = point_size * resolution / 72</tt><br>
          <tt>pixel_coord = grid_coord * pixel_size / EM_size</tt>
        </center></p>
      </li>
      <li>
        <p>The greater the EM size is, the larger resolution the designer
        can use when digitizing outlines.  For example, in the extreme
        example of an EM size of 4&nbsp;units, there are only 25&nbsp;point
        positions available within the EM square which is clearly not
        enough.  Typical TrueType fonts use an EM size of 2048&nbsp;units;
        Type&nbsp;1 PostScript fonts have a fixed EM size of 1000&nbsp;grid
        units but point coordinates can be expressed as floating values.</p>
      </li>
    </ul>

    <p>Note that glyphs can freely extend beyond the EM square if the font
    designer wants so.  The EM is used as a convenience, and is a valuable
    convenience from traditional typography.</p>

    <p>Grid units are very often called <em>font units</em> or <em>EM
    units</em>.</p>

    <p><em>As said before, <tt>pixel_size</tt> computed in the above formula
    does not relate directly to the size of characters on the screen.  It
    simply is the size of the EM square if it was to be displayed.  Each
    font designer is free to place its glyphs as it pleases him within the
    square.  This explains why the letters of the following text have not
    the same height, even though they are displayed at the same point size
    with distinct fonts:</em>

    <p><center>
      <img src="body_comparison.png"
           height=40 width=580
           alt="Comparison of font heights">
    </center></p>

    <p>As one can see, the glyphs of the Courier family are smaller than
    those of Times New Roman, which themselves are slightly smaller than
    those of Arial, even though everything is displayed or printed at a size
    of 16&nbsp;points.  This only reflects design choices.</p>


    <a name="section-3">
    <h3>
      3. Hinting and Bitmap rendering
    </h3>

    <p>The outline as stored in a font file is called the "master" outline,
    as its points coordinates are expressed in font units.  Before it can be
    converted into a bitmap, it must be scaled to a given size/resolution.
    This is done through a very simple transformation, but always creates
    undesirable artifacts, e.g. stems of different widths or heights in
    letters like "E" or "H".</p>

    <p>As a consequence, proper glyph rendering needs the scaled points to
    be aligned along the target device pixel grid, through an operation
    called <em>grid-fitting</em> (often called <em>hinting</em>).  One of its
    main purposes is to ensure that important widths and heights are
    respected throughout the whole font (for example, it is very often
    desirable that the "I" and the "T" have their central vertical line of
    the same pixel width), as well as to manage features like stems and
    overshoots, which can cause problems at small pixel sizes.</p>

    <p>There are several ways to perform grid-fitting properly; most
    scalable formats associate some control data or programs with each glyph
    outline.  Here is an overview:</p>

    <ul>
      <li>
        <p><em>explicit grid-fitting</em></p>

        <p>The TrueType format defines a stack-based virtual machine, for
        which programs can be written with the help of more than
        200&nbsp;opcodes (most of these relating to geometrical operations).
        Each glyph is thus made of both an outline and a control program to
        perform the actual grid-fitting in the way defined by the font
        designer.</p>
      </li>
      <li>
        <p><em>implicit grid-fitting (also called hinting)</em></p>

        <p>The Type&nbsp;1 format takes a much simpler approach: Each glyph
        is made of an outline as well as several pieces called
        <em>hints</em> which are used to describe some important features of
        the glyph, like the presence of stems, some width regularities, and
        the like.  There aren't a lot of hint types, and it is up to the
        final renderer to interpret the hints in order to produce a fitted
        outline.</p>
      </li>
      <li>
        <p><em>automatic grid-fitting</em></p>

        <p>Some formats simply include no control information with each
        glyph outline, apart font metrics like the advance width and height.  It
        is then up to the renderer to "guess" the more interesting features
        of the outline in order to perform some decent grid-fitting.</p>
      </li>
    </ul>

    <p>The following table summarises the pros and cons of each scheme.</p>

    <center>
      <table width="90%"
             bgcolor="#CCCCCC"
             cellpadding=5>
      <tr bgcolor="#999999">
        <td>
          <center>
            <b>grid-fitting scheme</b>
          </center>
        </td>
        <td>
          <center>
            <b>advantages</b>
          </center>
        </td>
        <td>
          <center>
            <b>disadvantages</b>
          </center>
        </td>
      </tr>

      <tr>
        <td valign=top>
          <center>
            <b>explicit</b>
          </center>
        </td>

        <td valign=top>
          <p><b>Quality.</b> Excellent results at small sizes are possible.
          This is very important for screen display.</p>

          <p><b>Consistency.</b> All renderers produce the same glyph
          bitmaps.</p>
        </td>

        <td valign=top>
          <p><b>Speed.</b> Interpreting bytecode can be slow if the glyph
          programs are complex.</p>

          <p><b>Size.</b> Glyph programs can be long.</p>

          <p><b>Technical difficulty.</b>
          It is extremely difficult to write good hinting
          programs.  Very few tools available.</p>
        </td>
      </tr>
      <tr>
        <td valign=top>
          <center>
            <b>implicit</b>
          </center>
        </td>

        <td valign=top>
          <p><b>Size.</b> Hints are usually much smaller than explicit glyph
          programs.</p>

          <p><b>Speed.</b>
          Grid-fitting is usually a fast process.</p>
        </td>

        <td valign=top>
          <p><b>Quality.</b> Often questionable at small sizes.  Better with
          anti-aliasing though.</p>

          <p><b>Inconsistency.</b> Results can vary between different
          renderers, or even distinct versions of the same engine.</p>
        </td>
      </tr>

      <tr>
        <td valign=top>
          <center>
            <b>automatic</b>
          </center>
        </td>

        <td valign=top>
          <p><b>Size.</b> No need for control information, resulting in
          smaller font files.</p>

          <p><b>Speed.</b> Depends on the grid-fitting algorithm.  Usually
          faster than explicit grid-fitting.</p>
        </td>

        <td valign=top>
          <p><b>Quality.</b> Often questionable at small sizes.  Better with
          anti-aliasing though.</p>

          <p><b>Speed.</b> Depends on the grid-fitting algorithm.</p>

          <p><b>Inconsistency.</b> Results can vary between different
          renderers, or even distinct versions of the same engine.</p>
        </td>
      </tr>
      </table>
    </center>

  <p><hr></p>

  <center>
  <table width="100%"
         border=0
         cellpadding=5>
  <tr bgcolor="#CCFFCC"
      valign=center>
    <td align=center
        width="30%">
      <a href="glyphs-1.html">Previous</a>
    </td>
    <td align=center
        width="30%">
      <a href="index.html">Contents</a>
    </td>
    <td align=center
        width="30%">
      <a href="glyphs-3.html">Next</a>
    </td>
  </tr>
  </table>
  </center>

</td></tr>
</table>
</center>

</body>
</html>
